Hot water cools from $60^{\circ} C$ to $50^{\circ} C$ in the first $10 \ min$ and to $42^{\circ} C$ in the next $10 \ min$. Then the temperature of the surroundings is (in $^{\circ} C$)

In an experiment to verify Newton's law of cooling,a graph is plotted between the temperature difference $(\Delta T)$ of the water and surroundings and time as shown in the figure. The initial temperature of water is taken as $80^{\circ}C$. The value of $t_{2}$ as mentioned in the graph will be...........

Two solid spheres $A$ and $B$ made of the same material have radii $r_A$ and $r_B$ respectively. Both the spheres are cooled from the same temperature under the conditions valid for Newton's law of cooling. The ratio of the rate of change of temperature of $A$ and $B$ is :

$A$ cup of tea cools from $65.5 ^\circ C$ to $62.5 ^\circ C$ in $1$ minute in a room at $22.5 ^\circ C$. How long will the same cup of tea take,in minutes,to cool from $46.5 ^\circ C$ to $40.5 ^\circ C$ in the same room? (Choose the nearest value)

$A$ can is taken out from a refrigerator at $0^{\circ}C$. The atmospheric temperature is $25^{\circ}C$. If $t_1$ is the time taken to heat from $0^{\circ}C$ to $5^{\circ}C$ and $t_2$ is the time taken to heat from $10^{\circ}C$ to $15^{\circ}C$,then:

$A$ very thin metallic shell of radius $r$ is heated to temperature $T$ and then allowed to cool. The rate of cooling of the shell is proportional to ........